The need for highly realistic graphics in modern computer applications has increased greatly over the past years. Applications such as computer aided design (CAD) and computer games, for example, require realistic and accurate graphical representations of characters, objects, scenery, colors, shading, etc. to provide the computer user with the ability to successfully execute the application in the desired manner.
It has become essential for today's computer applications to use three-dimensional (3D) geometry when simulating the features of the graphic elements that are to be displayed. Typically, each graphic element or object is broken down into a collection/combination of graphic “primitives” such as e.g., lines, triangles, polygons and/or ellipses. Each primitive is comprised of 3D information referred to as vertices. Each vertex of the group of vertices is represented by a floating point number. The vertices will be transformed by matrices (e.g., tessellation, geometric transformations, lighting, projection, etc.).
The complexity of the floating point operations can be illustrated by examining the typical floating point number used in today's graphical computer applications. Referring to FIG. 1 the format for a conventional floating point number 10 is now described. The illustrated format complies with the IEEE standard 754 single precision floating point format. The floating point number 10 comprises a sign bit 12 (denoted as “S”), an exponent portion 14 (denoted as “E”) and a mantissa portion 16 (denoted as “M”). Floating point numbers 10 represented in this format have a value V, where V is defined as:V=(−1)S−127*2E*(1.M).  (1)
The sign bit 12 (S) represents the sign of the entire number 10, while the mantissa portion 16 (M) is a 23-bit number with an implied leading 1. The exponent portion 14 (E) is an 8-bit value that represents the true exponent of the number 10 offset by a bias, which in the illustrated format is 127. The floating point number 10 may have values V with exponents ranging from −127 to +128. Thus, for each vertex in a graphic component such as a primitive, several calculations are required to properly manipulate the floating point sign bit 12 and the exponent and mantissa portions 14, 16 of the vertex. These calculations are further compounded because each graphic component has several vertices.
Since many of today's computer applications operate in real-time, the transformation of the 3D image and the formation from 3D to 2D (two-dimensional) must be performed in an expedited manner. Dedicated graphics pipelines are often used to speed up the necessary calculations and transformations. These pipelines comprise floating point arithmetic designed to perform tessellation, geometrical transformations, lighting, clipping, projection, polygon setup and rasterization. Tessellation is the process of breaking down graphic elements into primitives. Geometrical transformations include the translation, rotation and scaling of the primitives. Lighting is the computing, for each vertex, of the result of the interaction between ambient, diffuse or specular light and the primitive's material properties. Clipping involves deleting portions of the primitives that will not fit within the displayable area of the display screen. Projection is the projection of the 3D images onto the display plane. Polygon setup is the computation of colors along the edges of the primitives and rasterization is the transformation of the 3D image to a set of colored pixels.
A vertex engine or shader is typically responsible for the lighting and geometric transformation operations. A repeated feature of these vertex engine operations is the computationally intensive transformation of the floating point vertex data vectors (e.g., single precision floating point numbers 10 illustrated in FIG. 1) using matrix transformations. A key element of the matrix transformation is a three or four component dot product of two vectors. Thus, to speed up the operation of the vertex engine and the overall pipeline, there is a need and desire to perform four component dot product computations as fast as possible. One way to do so, would be to compute the four component dot products during a single pass through the vertex engine—something that is not done in today's computer arithmetic pipelines and systems. Accordingly, there is a need and desire for a floating point pipeline that is capable of computing a four component dot product in a single pass through the vertex engine (i.e., the vertex data passes through the vertex engine a single time and all the required computations are performed during that same time).
There is also a need and desire for a floating point pipeline that is capable of computing a four component dot product in a single pass through the vertex engine without substantially increasing the cost and amount of hardware required to implement the pipeline.